To determine whether the data represent exponential or logistic growth, we need to consider how the population size changes over the given years. Here's a step-by-step analysis:
1. Listing the Data:
- Years: 2012, 2013, 2014, 2015, 2016
- Population Sizes: 5, 25, 125, 185, 205
2. Population Growth Rates:
- Calculate the growth rate for each year by comparing consecutive population sizes:
[tex]\[
\text{Growth rate from 2012 to 2013} = \frac{25}{5} = 5
\][/tex]
[tex]\[
\text{Growth rate from 2013 to 2014} = \frac{125}{25} = 5
\][/tex]
[tex]\[
\text{Growth rate from 2014 to 2015} = \frac{185}{125} = 1.48
\][/tex]
[tex]\[
\text{Growth rate from 2015 to 2016} = \frac{205}{185} = 1.11
\][/tex]
3. Analyzing Growth Types:
- Exponential Growth: This type of growth would show a constant growth rate; the population would multiply by the same factor every year.
- Logistic Growth: This growth starts exponentially but then slows down as the population approaches a carrying capacity, causing the growth rate to decrease over time.
4. Growth Rate Pattern:
- Initially, the growth rates (5 from 2012 to 2013 and from 2013 to 2014) are significantly high, suggesting rapid initial growth.
- The growth rates then decrease (1.48 from 2014 to 2015 and 1.11 from 2015 to 2016), indicating that the population growth is slowing down.
5. Conclusion:
- Given the high initial growth rate followed by a significant decrease in subsequent growth rates, the data suggest that the population growth starts off rapidly and then slows down, which is characteristic of logistic growth.
Therefore, the data in the table represent Logistic growth.
